Flame height

The flame height is intimately related to the entrainment rate. Indeed, one is dependent on the other. For a turbulent flame that can entrain n times the air needed for combustion (Equation (10.34)), and r, the mass stoichiometric oxygen to fuel ratio, the mass rate of fuel reacted over the flame length, Zf, is 

Substitution of Equation (10.46b) with z = Zf gives a correlation for flame height. The value n is found by a best fit of data in air (To2j00 = 0.233) as 9.6. The implicit equation for Zf in air is 

An alternative, explicit equation for Zf given by Heskestad [24], based on the virtual origin correction (see Equation (10.40)), is given as 

When determining flame height, an assumption that the flame is a solid gray emitter with a well-defined cylindrical shape is made for ease of calculation. The cylinder may be straight or tilted as a result of wind. For pool fires, the flame height above the fire source can be determined by (Heskestad, 1981 1983)  

Additional discussion on the effect of wind and tilt of flame can be found in the SPFE Handbook (Beyler, 2002). 

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The smoke point corresponds to the maximum possible flame height (without smoke formation) from a standardized lamp (NF M 07-028). The values commonly obtained are between 10 and 40 mm and the specifications for TRO fix a minimum threshold of 25 mm. The smoke point is directly linked to the chemical structure of the fuel it is high, therefore satisfactory, for the linear paraffins, lower for branched paraffins and much lower still for naphthenes and aromatics. 

The luminometer index (ASTM D 1740) is a characteristic that is becoming less frequently used. It is determined using the standard lamp mentioned above, except that the lamp is equipped with thermocouples allowing measurement of temperatures corresponding to different flame heights, and a photo-electric cell to evaluate the luminosity. The jet fuel under test is compared to two pure hydrocarbons tetraline and iso-octane to which are attributed the indices 0 and 100, respectively. The values often observed in commercial products usually vary between 40 and 70 the official specification is around 45 for TRO. 

Smoke point NF M 07-028 ISO 3014 ASTM D 1322 Mciximum flame height with no smoking... 

This experiment describes a fractional factorial design used to examine the effects of flame height, flame stoichiometry, acetic acid, lamp current, wavelength, and slit width on the flame atomic absorbance obtained using a solution of 2.00-ppm Ag+. 

For a line spark source, the flame volume is initially cylindrical with the cylinder length equal to the separation distance between the electrodes. Thus, for a cylindrical flame, = e, and the critical ignition volumes are equation 7 for a spherical flame and equation 8 for a cylindrical flame where = critical ignition volume, m /kg e = thickness of flame front, m and d = flame height, m. 

The Displacement Distance theory suggests that since the stmcture of the flame is only quantitatively correct, the flame height can be obtained through the use of the displacement length or "displacement distance" (35,36) (eq. 12), where h = flame height, m V = volumetric flow rate, m /s and D = diffusion coefficient. 

Combustion chemistry in diffusion flames is not as simple as is assumed in most theoretical models. Evidence obtained by adsorption and emission spectroscopy (37) and by sampling (38) shows that hydrocarbon fuels undergo appreciable pyrolysis in the fuel jet before oxidation occurs. Eurther evidence for the existence of pyrolysis is provided by sampling of diffusion flames (39). In general, the preflame pyrolysis reactions may not be very important in terms of the gross features of the flame, particularly flame height, but they may account for the formation of carbon while the presence of OH radicals may provide a path for NO formation, particularly on the oxidant side of the flame (39). 

Consider the case of the simple Bunsen burner. As the tube diameter decreases, at a critical flow velocity and at a Reynolds number of about 2000, flame height no longer depends on the jet diameter and the relationship between flame height and volumetric flow ceases to exist (2). Some of the characteristics of diffusion flames are illustrated in Eigure 5. 

Fig. 5. Effects of nozzle velocity on flame appearance in laminar and tuibulent flow (a), flame appearance (b), flame height and break-point height (40).

The fire at the ruptured pipe produced flame heights of up to 120 m (400 ft). It was left burning until the valves were shut off to isolate the failed pipe section. 

The surface-emissive powers of fireballs depend strongly on fuel quantity and pressure just prior to release. Fay and Lewis (1977) found small surface-emissive powers for 0.1 kg (0.22 pound) of fuel (20 to 60 kW/m 6300 to 19,000 Btu/hr/ ft ). Hardee et al. (1978) measured 120 kW/m (38,000 Btu/hr/ft ). Moorhouse and Pritchard (1982) suggest an average surface-emissive power of 150 kW/m (47,500 Btu/hr/ft ), and a maximum value of 300 kW/m (95,000 Btu/hr/ft ), for industrialsized fireballs of pure vapor. Experiments by British Gas with BLEVEs involving fuel masses of 1000 to 2000 kg of butane or propane revealed surface-emissive powers between 320 and 350 kW/m (100,000-110,000 Btu/hr/ft Johnson et al. 1990). Emissive power, incident flux, and flame height data are summarized by Mudan (1984). 

Stewart, F. R. 1964. Linear flame heights for various fuels. Combustion and Flame 8 171-178. 

The subject of flash fires is a highly underdeveloped area in the literature. Only one mathematical model describing the dynamics of a flash fire has been published. This model, which relates flame height to burning velocity, dependent on cloud depth and composition, is the basis for heat-radiation calculations. Consequently, the calculation of heat radiation from flash fires consists of determination of the flash-fire dynamics, then calculation of heat radiation. 

Flash-fire dynamics are determined by a model which relates flame height to a cloud s depth and composition, and to flame speed. On the basis of experimental observations, flame speed was roughly related to wind speed. Flame height can be computed from the following expression ... 

H = visible flame height S = 2.3 X = flame speed = wind speed d = cloud depth g = gravitational acceleration po = fuel-air mixture density pj = density of air r = stoichiometric air-fuel mass ratio a = expansion ratio for stoichiometric combustion under constant pressure (typically 8 for hydrocarbons)... 

Calculate the flame height from the cloud depth d, gravitational acceleration g, S (P[Pg.279]

In addition to flame height, other flame dimensions must also be known. In general, flame shape must be assumed. A flame s surface area and position both vary during the course of the flash fire, so, if based on manual calculations, flame shape... 

Kerosene lamps have a flat cloth wick. Flame height is determined by the height of the wick, which is controlled by a ratchet knob. A glass chimney ensures both safety and a stable, draft-free flame. 

Ignition sources of BS 5852 Parts 1 and 2 Theoretical heat of combustion approx. Flame height Flame temp. Local heat flux. Rate of burning Duration of flaming ... 

Delichatsios, M. A., "Flame Heights in Turbulent Wall Fires with Significant Flame Radiation", Comb. Sci. Tech., 39, p. 195, 1984. 

The initial region ignited is 0.5 cm and the ambient temperature is 20 °C. The flame height during flame spread is given by xf = (0.01m2/kW)g, where Q is the energy release rate per unit width in kW/m. 

Calculate the upward spread velocity at 0.5 m from the floor. The flame height from the floor is 1.8 m and the heat flux from the flame is estimated at 3 W/cm2. 

If we had significant momentum or mass flow rate at the origin, the plume would resort to a jet and the initial momentum would control the entrainment as described by Equation (10.3). This jet behavior will have consequences for the behavior of flame height compared to the flame height from natural fires with negligible initial momentum. 

The coefficient Ce depends on Xr and is 0.17 for Xr = 0.2 for the empirical constants of Table 10.1 Zukoski [8] reports 0.21 and Ricou and Spalding [21] report 0.18. For the far-held, valid above the flame height, Heskestad [22] developed the empirical equation ... 

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